The motivation behind obs2 is that, in various practical learning tasks, the data satisfy some special properties that make the learning process simpler. For instance, it is a common principle to use classification with margin where the points in the dataset have a safe gap from the decision boundary. Such properties induce data-dependent assumptions that the traditional PAC learning theory framework provably fails to express.
In fact, existing data-dependent analyses diverge from the standard PAC model [1]}, [2]} and provide problem-specific approaches. Thus, there is a need for a formal framework that allows us to express such data-dependent restrictions and study these problems in a unified and principled way. Recently, [3]} proposed an elegant extension of the binary PAC model to handle such tasks via the framework of partial concept classes. As an intuitive example, a halfspace with margin is a partial function that is undefined inside the forbidden margin and is a well-defined halfspace outside the margin boundaries.
